Smooth orthogonal drawings of planar graphs

Muhammad Jawaherul Alam, Michael A. Bekos, Michael Kaufmann, Philipp Kindermann, Stephen G Kobourov, Alexander Wolff

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Abstract

In smooth orthogonal layouts of planar graphs, every edge is an alternating sequence of axis-aligned segments and circular arcs with common axis-aligned tangents. In this paper, we study the problem of finding smooth orthogonal layouts of low edge complexity, that is, with few segments per edge. We say that a graph has smooth complexity k - for short, an SC k -layout - if it admits a smooth orthogonal drawing of edge complexity at most k. Our main result is that every 4-planar graph has an SC2-layout. While our drawings may have super-polynomial area, we show that for 3-planar graphs, cubic area suffices. We also show that any biconnected 4-outerplane graph has an SC1-layout. On the negative side, we demonstrate an infinite family of biconnected 4-planar graphs that require exponential area for an SC 1-layout. Finally, we present an infinite family of biconnected 4-planar graphs that do not admit an SC1-layout.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages144-155
Number of pages12
Volume8392 LNCS
ISBN (Print)9783642544224
DOIs
Publication statusPublished - 2014
Event11th Latin American Theoretical Informatics Symposium, LATIN 2014 - Montevideo, Uruguay
Duration: Mar 31 2014Apr 4 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8392 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other11th Latin American Theoretical Informatics Symposium, LATIN 2014
CountryUruguay
CityMontevideo
Period3/31/144/4/14

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ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Alam, M. J., Bekos, M. A., Kaufmann, M., Kindermann, P., Kobourov, S. G., & Wolff, A. (2014). Smooth orthogonal drawings of planar graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8392 LNCS, pp. 144-155). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8392 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-642-54423-1_13